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A two-digit locker combination has two nonzero digits and no digit is repeated in any combination.

Event A = the first digit is less than 7

Event B = the second digit is less than 7

If a combination is picked at random with each possible locker combination being equally likely, what is P(B|A) expressed in simplest form?

a)5/9 b)5/8 c)2/3 d)3/4 WILL MARK BRAINLIEST AND ADD 100 MORE POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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osikbro

Answer:

Answer choice C

Step-by-step explanation:

Similarly to the previous problem, there are two possibilities. In the first possibility, the chance of picking a digit lower than 7 is 6/9 or 2/3, because there are 6 digits below 7 and 9 digits in total. In this scenario, the probability of the second digit being below 7 is 5/8, since one of the digits has already been taken. The probability here is 5/8*6/9=5/12. In the other scenario, the probability of picking a number higher than 7 is 3/9 or 1/3. In this scenario, the probability of picking below 7 for the second digit is 6/8 or 3/4, because one of the digits has not been taken. 3/9*6/8= 1/4. Adding these two together, you get 8/12=2/3, or answer choice C. Hope this helps!

If a combination is picked at random with each possible locker combination being equally likely, then P(B|A) is expressed in simplest form as option (c.) 2/3

Probability

  • Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true

What are steps to solve this problem?

Steps to solve this problem is as follow

  • For Event A:

Chance of picking a digit lower than 7 = 6/9 because of 6 digit lower than 7 and there are total 9 numbers only

Chance of the second digit being below 7 = 5/8 because one digit is already been taken

So here probability P(A) = (6/9)*(5/8) = 0.4167

  • For Event B:

Chances of picking a number higher than 7 = 3/9

Chances of picking below 7 for the second digit is = 6/8  because one of the digit has not been taken

So here probability P(B) = (3/9)*(6/8) = 0.2500

  • Now adding, P(A) & P(B)

P(A) + P(B) = 0.4167 + 0.25 = 0.6667 = 2/3

P(B|A) expressed in simplest form as 2/3

Learn more about probability here:

https://brainly.com/question/25870256

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