Find the smallest possible value of P(A and B)

Watch
TSR360
Badges: 11
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#1
Report Thread starter 1 year ago
#1
Q: http://prntscr.com/xmzsml

If A and B are mutually exclusive then they cannot happen together, so the smallest possible value would be 0 or else it would be (0.9 x 0.7) = 0.63. However, in the textbook it says 0.6...
0
reply
mqb2766
Badges: 19
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#2
Report 1 year ago
#2
(Original post by TSR360)
Q: http://prntscr.com/xmzsml

If A and B are mutually exclusive then they cannot happen together, so the smallest possible value would be 0 or elswe it would be (0.9 x 0.7) = 0.63. However, in the textbook it says 0.6...
What do they sum to? What are the laws of probability?
Independence is an important property for probability functions, but the intersection can be less or more than that value. It's not a bound. In a Venn diagram, the sets can overlap anything between 0 and min(A,B).
Last edited by mqb2766; 1 year ago
1
reply
davros
Badges: 16
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#3
Report 1 year ago
#3
(Original post by TSR360)
Q: http://prntscr.com/xmzsml

If A and B are mutually exclusive then they cannot happen together, so the smallest possible value would be 0 or else it would be (0.9 x 0.7) = 0.63. However, in the textbook it says 0.6...
It might help you to remember the rule P(A u B) = P(A) + P(B) - P(A n B) (you can see this from a Venn diagram).

Remember that P(A u B) is a probability, so that its max value is 1. What does that tell you about P(A n B)?
1
reply
GlowInTheDark
Badges: 7
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#4
Report 1 year ago
#4
The probability that A happens is 0.9 and that B happens is 0.7. The minimum possible probability is (1-0.9) + (1-0.7) which would get the value of 0.4, 1-0.4 = 0.6
1
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

When did you submit your Ucas application if you applied to go to university this year?

September 2021 (33)
7.16%
October 2021 (209)
45.34%
November 2021 (52)
11.28%
December 2021 (60)
13.02%
January 2021 (51)
11.06%
I still haven't submitted it yet! (41)
8.89%
Something else (15)
3.25%

Watched Threads

View All