Answer:
11/16
Step-by-step explanation:
"at least 2 times" means 2 or 3 or all 4 times.
which is the opposite (1 - ...) of getting it 0 or 1 time.
the probabilty of getting heads in one attempt is 1/2.
as is the probability to get tails. no other result is possible.
the probability to get 2 heads (or 2 tails) is
1/2 × 1/2 = 1/4
the probability to get 4 heads or 4 tails is
1/2 × 1/2 × 1/2 × 1/2 = 1/16
so, the probability to get at least 2 heads in 4 attempts is the same as
1 - the probability to get 4 tails (0 heads) - the probability to get exacting 1 heads =
= 1 - 1/16 - the probability to get exactly 1 heads
the probability to get exactly 1 heads (and therefore 3 tails) is in one possible combination of coin results
1/2 × 1/2×1/2×1/2 = 1/16 (it is funny with coins and only 2 possible results).
but how often can we pick 1 out of 4 (how many combinations of C(4, 1) are possible) ? 4.
so, we need to multiply 1/16 by 4 = 4/16 to get that overall probability.
so, now again, the probability to get at least 2 heads in 4 attempts is
1 - 1/16 - 4/16 = 1 - 5/16 = 16/16 - 5/16 = 11/16
