Question

For the given pair of events A and​ B, complete parts​ (a) and​ (b) below.

​A: When a baby is​ born, it is a

boy

.

​B: When a

17

​-sided

die is​ rolled, the outcome is

5

.

a. Determine whether events A and B are independent or dependent.​ (If two events are technically dependent but can be treated as if they are independent according to the​ 5% guideline, consider them to be​ independent.)

b. Find​ P(A and​ B), the probability that events A and B both occur.

b. The probability that events A and B both occur is _____________________

Answer 1

Answer:

a)

Given,

A be the event that wen a baby is born it is a boy

i.e.,

P(A) = 1/2

B be the event that 7 sided die is rolled and the outcome is 5

i.e.,

P(B) = 1/5

Here we can say that A and B are independent as rolling of die with new born boy or gender doesn't matter.

b)

To determine the P(A and B)

P(A and B) = P(A).P(B) ------------->(1)

Here P(A) = 1/2

P(B) = 1/5

substitute P(A) & P(B) in eq (1)

P(A B) = 1/2 * 1/5

= 1/10

P(A B) = 0.1