Question

A fair coin is tossed 4 times. define the sample space corresponding to this random experiment. also give the subsets corresponding to the following events and find the respective probabilities.

a) more heads than tails are obtained.
b) tails occur on the even are obtained.

Answer 1

A fair coin tossed 4 times creates a sample space with 16 outcomes. The subsets for more heads than tails are 5 outcomes, giving a probability of 5/16. For tails on even tosses, there are 4 outcomes, resulting in a probability of 1/4.

Step-by-step explanation:

When a fair coin is tossed 4 times, the sample space consists of 16 possible outcomes (24), since each toss has 2 possible outcomes (heads or tails). The sample space can be represented as follows:

• HHHH
• HHHT
• HHTH
• HHTT
• HTHH
• HTHT
• HTTH
• HTTT
• THHH
• THHT
• THTH
• THTT
• TTHH
• TTHT
• TTHH
• TTTT

For the event (a) where more heads than tails are obtained, the subsets are {HHHH, HHHT, HHTH, HTHH, THHH}. There are 5 outcomes in which there are more heads than tails out of the total 16 outcomes, so the probability of this event is P(a) = 5/16.

For the event (b) where tails occur on the even tosses, the subsets are {HTHT, HTTT, THTT, THHT}. There are 4 outcomes in which tails occur on even tosses out of the total 16 outcomes, so the probability of this event is P(b) = 4/16 or 1/4.