If a fair coin is tossed twice, find the probability of getting 'at most

Q) If a fair coin is tossed twice, find the probability of getting ‘at most one head’.

Ans:

When we toss 2 fair coins, here are the possible outcomes:

HH, HT, TH, TT

Here, we need to get at most 1 head.

It means we will include outcomes of getting 1 head and no head.

Since outcome of getting 2 heads (HH) has more than 1 head, and hence, it will not be considered.

Now, outcomes of getting 1 head = HT & TH i.e. 2 outcomes

and outcomes of no head = TT i.e. 1 outcomes

Therefore, the favourable outcomes = 2 + 1 = 3

Hence, the probability of getting ‘at most one head’

= $\frac{Favourable ~ outcomes}{Total ~ outcomes}$ = $\frac{3}{4}$

Therefore, the probability of getting ‘at most one head’ is $\frac{3}{4}$ .

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