A coin is tossed 4 times Aat least 2 of the tosses are heads

A coin is tossed 4 times

A:at least 2 of the tosses are heads

B: The first and lst toss are the same

C: the second toss is tales and the third toss is heads

A.) P(A)

B.)P(B)

C.)P(AnB)

Sample space: (HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, THTH, HTTH, THHT, TTHH, TTTH, TTHT, THTT, HTTT, TTTT) 16 events

A:at least 2 of the tosses are heads. These include: (HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, THTH, HTTH, THHT, TTHH) 11 events

B: The first and last toss are the same. These include: (HHHH, HHTH, HTHH, HTTH, THHT, TTHT, THTT, TTTT) 8 events

C: the second toss is tales and the third toss is heads. These include: (HTHH, HTHT, TTHH, TTHT) 4 events

A.) P(A) = N(E)/N(S) = 11/16 or 0.6875

B.)P(B) = N(E)/N(S) = 8/16 or 0.5

C.)P(AnB)

The events included in both A and B are (HHHH, HHTH, HTHH, HTTH, THHT) 5 events

So the probability is N(E)/N(S) = 5/16 or 0.3125