Three unbiased coins are tossed simultaneously. Find the probability of getting
at most 2 heads.

Options

A. `1/8`
B. `7/8`
C. `3/8`
D. `1/4`

Answer

B

Explanation

When 3 coins are tossed simultaneously, all possible outcomes are HHH, HHT, HTH, THH, HTT, THT, TTH, TTT.
Total number of possible outcomes = 8.
(i) Let `E_(1)` be the event of getting exactly 2 heads.
Then, the favourable outcomes are HHT, HTH, THH.
Number of favourable outcomes = 3.
` :. ` P(getting exactly 2 heads) = ` P(E_(1)) = 3/8`.
(ii) Let `E_(2)` be the event of getting at least 2 heads.
Then, `E_(2)` is the event of getting 2 or 3 heads.
So, the favourable outcomes are
HHT, HTH, THH, HHH.
Number of favourable outcomes = 4.
`:. ` P(getting at least 2 heads) = `P(E_(2)) = 4/8 = 1/2`.
(iii) Let `E_(3)` be the event of getting at most 2 heads.
Then, `E_(3)` is the event of getting 0 or 1 head or 2 heads.
So, the favourable outcomes are
TTT, HTT, THT, TTH, HHT, HTH, THH.
Number of favourable outcomes = 7.
`:. ` P(getting at most 2 heads ) = `P(E_(3)) = 7/8`.