GMAT question - The probability that a certain coin turns up heads w... - Review

Type: Problem Solving

Difficulty: 4 star rating

The probability that a certain coin turns up heads when it is flipped is mathematical expression. If this coin is flipped 3 times then what is the probability that heads turns up at least twice?

  1. mathematical expression
  2. mathematical expression
  3. mathematical expression
  4. mathematical expression
  5. mathematical expression

Explanation

You are asked to work out what the probability of heads being turning up 2 or 3 times when a coin is flipped 3 times.

Since each coin can only turn up heads or tails, this is the same as asking what the probability of tails not turning up 2 or 3 times when a coin is flipped 3 times.

By symmetry this must be mathematical expression which makes C the correct answer.

If you are unconvinced by this argument then the slightly longer way of doing it is to say

P(2 or more heads) = P(2 heads) + P(3 heads)

The total number of possible outcomes is 2 x 2 x 2 = 8 and there are three ways of getting two heads (HHT, HTH, THH) and one way of getting three heads (HHH) so

mathematical expression

Which gives us the same answer as before.

Comments (2):

  1. i am still not getting this.

    sphirioboy on 5 Apr 2009 (permalink)

  2. The first part: P(2 or more heads), we must consider the permutation factor: i.e HHT, HTH or THH, which gives us 1/8 x 3 = 3/8

    The second part is pretty straight forward: P(3 heads) = 1/8

    Adding the two togehter you'll get 3/8 + 1/8 = 4/8 = 1/2.

    Draw a tree diagram to make it look feasible and easy.

    bhalim on 21 Nov 2009 (permalink)

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