Joe and Maxine are playing a game where they flip a fair coin four times and try to predict the outcomes. Joe thinks that the probability of getting exactly two heads in the four flips is greater than the probability of getting heads on both the first and second flips. Maxine disagrees. She thinks that the two probabilities are equal.

Joe is right, the probability of getting exactly two heads in the four flips is greater than the probability of getting heads on both the first and second flips.

Step-by-step explanation:

First creating a sample space :

, HHHT, TTHT, HTTH, THHH, , TTTH, TTHH, HTHH, HTTT, HHTT, THTH, HHTH, THTT, HTHT, THHT

A fair coin (H - HEAD, T - TAIL)

Probability = (required outcome / possible outcome)

Probability getting exactly two heads in first four flips:

= 6/16 = 3/8

Probability of getting head on both the first and second flips :

= 4/16 = 1/4

Therefore Joe is right, the probability of getting exactly two heads in the four flips is greater than the probability of getting heads on both the first and second flips.

blue marble is 15 times out of 50 = 15/50 reduces to 3/10

landing on tails is 24 out of 50 = 24/50 reduces to 12/25

to find the probability of both multiply together:

3/10 x 12/25 = 3 x 12 / 10 x 25 = 36/250

if you multiplied the numerator and denominator by 10 you get 360/2500.

the answer is 360/2500