hard probability question

OP

Original post by Tubbz

You're definitely wrong, a probability of greater than 1 should ring alarm bells. What have you tried?

Reply 3

OP

hi i need help.

(non-calculator)

Mr. Lucky plays two games.

The two games are Game A and Game B.

Playing Game A and Playing Game B are independent events.

The probability Mr.lucky wins both games is 9/25 (0.36)

The probability that Mr. Lucky wins Game B is four times greater than him losing Game A

Find the probability that Mr. lucky wins only one of the two games.

i got 2.98 - but i think i am wrong

Attachment not found

(edited 6 years ago)

Reply 4

Original post by Maths1up

hi i need help.

(non-calculator)

Mr. Lucky plays two games.

The two games are Game A and Game B.

Playing Game A and Playing Game B are independent events.

The probability Mr.lucky wins both games is 9/25 (0.36)

The probability that Mr. Lucky wins Game B is four times greater than him losing Game A

Find the probability that Mr. lucky wins only one of the two games.

i got 2.98 - but i think i am wrong

This question seems very hard for GCSE...however:

Let a and b respectively denote the probability that Mr.Lucky wins game a and game b. Can you use the information to find two simultaneous equations in a and b? I'll put the answers in a spoiler

Spoiler

Reply 5

OP

Original post by theOldBean

This question seems very hard for GCSE...however:

Let a and b respectively denote the probability that Mr.Lucky wins game a and game b. Can you use the information to find two simultaneous equations in a and b? I'll put the answers in a spoiler

Spoiler

i understand what you did but instead i made a quadratic equation instead
and yes i know its a hard question, my teacher gave us part of a grade 9

(edited 6 years ago)

Reply 6

moz4rt

10

Original post by Maths1up

If my working out is correct your x value is incorrect. We have 2 ways of calculating the probability of winning A which we can then equate the solve for our unknown.

Reply 7

What you did seems reasonable. I like the tree diagram as it shows me what you are thinking. In your tree diagram, you are implicitly using the fact that the two games are independent, because you have 1-4x and 4x in BOTH of the 'game B' branches.

You then correctly obtained the quadratic 4x(1-x)=9/25, were x=P(lose game a)- but this quadratic has TWO roots. These are 0.1 and 0.9 (check this!)
How can you tell which of these is the 'correct' one to take?

(edited 6 years ago)

Reply 8

Original post by moz4rt

If my working out is correct your x value is incorrect. We have 2 ways of calculating the probability of winning A which we can then equate the solve for our unknown.

OP has made two separate threads, each containing this problem. It might be better to use just the other thread, which is here (I'll edit my post in a minute with the link):

EDIT: https://www.thestudentroom.co.uk/showthread.php?p=75523770&highlight=

title of thread is 'maths probability question'

(edited 6 years ago)

Reply 9

OP

Original post by theOldBean

What you did seems reasonable. I like the tree diagram as it shows me what you are thinking. In your tree diagram, you are implicitly using the fact that the two games are independent, because you have 1-4x and 4x in BOTH of the 'game B' branches.

You then correctly obtained the quadratic 4x(1-x)=9/25, were x=P(lose game a)- but this quadratic has TWO roots. These are 0.1 and 0.9 (check this!)
How can you tell which of these is the 'correct' one to take?

i square rooted 0.16 and that would give +/- 0.4
i chose the positive value as it made more sense as you cant have a negative probability

Reply 10

OP

Original post by moz4rt

If my working out is correct your x value is incorrect. We have 2 ways of calculating the probability of winning A which we can then equate the solve for our unknown.

what did you do?

Reply 11

In your working, you had +/-0.4 = x-0.5, so x=0.1 or 0.9. BOTH of these lie in the interval [0,1] so both can be probabilities. However, it turns out that only one of them is correct. Have a think about which one this might be.

Reply 12

OP

Original post by theOldBean

In your working, you had +/-0.4 = x-0.5, so x=0.1 or 0.9. BOTH of these lie in the interval [0,1] so both can be probabilities. However, it turns out that only one of them is correct. Have a think about which one this might be.

ohh i see what you mean. i dont know what do you thnik?

Reply 13

Original post by Maths1up

ohh i see what you mean. i dont know what do you thnik?

Well I already know how to solve the problem, so I'm not going to tell you :P. But here's a hint:

Spoiler

Reply 14

OP

Original post by theOldBean

Well I already know how to solve the problem, so I'm not going to tell you :P. But here's a hint:

Spoiler

so i was meant to take the negative value for x
i get 0.58 seems right

Reply 15

Original post by Maths1up

so i was meant to take the negative value for x
i get 0.58 seems right

EDIT: Yes, this is the correct answer. Well done :smile:

(edited 6 years ago)

Reply 16

OP