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Instead of calculating the probability of getting at least one head and at least one tail, let's calculate the probability of getting NO head and the probability of getting NO tail. We'll then subtract these values from 1 to get the answer.BTGmoderatorDC wrote:If six coins are flipped simultaneously, the probability of getting at least one heads and at least one tails is closest to
A) 3%
B) 6%
C) 75%
D) 94%
E) 97%
OA E
Source: Veritas Prep
When it comes to probability questions involving "at least," it's best to try using the complement.BTGmoderatorDC wrote:If six coins are flipped simultaneously, the probability of getting at least one heads and at least one tails is closest to
A) 3%
B) 6%
C) 75%
D) 94%
E) 97%
OA E
Source: Veritas Prep
\[?\,\,\, = \,\,\,1 - P\left( {{\text{in}}\,\,6\,\,{\text{flips}},\,\,6H\,\,{\text{or}}\,\,6T} \right)\,\,\, = \,\,\,1 - {?_{{\text{temporary}}}}\]BTGmoderatorDC wrote:If six coins are flipped simultaneously, the probability of getting at least one heads and at least one tails is closest to
A) 3%
B) 6%
C) 75%
D) 94%
E) 97%
Source: Veritas Prep
There are 2^6 = 64 ways the six coins could be flipped. Of the these 64 ways, only two of them (all heads and all tails) do not have at least one head or at least one tail. Therefore, the probability of getting at least one head and at least one tail is 62/64 = 0.96875 ≈ 97%.BTGmoderatorDC wrote:If six coins are flipped simultaneously, the probability of getting at least one heads and at least one tails is closest to
A) 3%
B) 6%
C) 75%
D) 94%
E) 97%
