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S2 binomial distribution question

S2 QUESTION.png

A six-sided die is biased. When the die is thrown the number 5 is twice as likely to appear as any other number. All the other faces are equally likely to appear. The die is thrown repeatedly.
Find the probability that (b) (i) the first 5 will occur on the sixth throw,

(ii) in the first eight throws there will be exactly three 5s.

I do not know how to do part b)i)
Original post by patterson
S2 QUESTION.png

A six-sided die is biased. When the die is thrown the number 5 is twice as likely to appear as any other number. All the other faces are equally likely to appear. The die is thrown repeatedly.
Find the probability that (b) (i) the first 5 will occur on the sixth throw,

(ii) in the first eight throws there will be exactly three 5s.

I do not know how to do part b)i)


It is just a Binomial distribution question. The number of 5's in 8 throws will have the Binomial distribution B(8,2/7) so probability of 3 5's will; be 8C3×(27)3×(57)5 ^8C_3 \times \left(\frac{2}{7}\right)^3 \times \left(\frac{5}{7} \right)^5
Reply 2
Original post by brianeverit
It is just a Binomial distribution question. The number of 5's in 8 throws will have the Binomial distribution B(8,2/7) so probability of 3 5's will; be 8C3×(27)3×(57)5 ^8C_3 \times \left(\frac{2}{7}\right)^3 \times \left(\frac{5}{7} \right)^5


Bit to late since I had my exam yesterday. But thanks
Reply 3
Original post by brianeverit
It is just a Binomial distribution question. The number of 5's in 8 throws will have the Binomial distribution B(8,2/7) so probability of 3 5's will; be 8C3×(27)3×(57)5 ^8C_3 \times \left(\frac{2}{7}\right)^3 \times \left(\frac{5}{7} \right)^5

why is it 2/7 and not 2/6?
Reply 4
Original post by tabzz1
why is it 2/7 and not 2/6?

probability of getting a 5 is 2 times more likely than the rest. we can say probability of getting 1, 2, 3, 4, or 6 is x and probability of getting a 5 is 2x. all of these probabilities add up to 1 so there is 7x in total. 7x = 1 so x=1/7. so chance of getting 5 is 2/7

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