First, group the 40 identical candies into 20 pairs. It doesn't matter how since the candies are identical. This grouping will ensure that any assigment will contain at least two candies.

Then think of the 20 groups a 20 beads on a string. We are looking to place 11 separators between them to obtain 12 segments, each with a varying number of beads between them. How many ways are there to place 11 separators to 19 potential spaces between beads? The asnwer is $n = {19\choose{11}}=75582$

5 0

3 years ago

The length of a phone conversation is normally distributed with a mean of 4 minutes and a standard deviation of 0.6 minutes. Wha

Arlecino [84]

The z-score for 5 minutes is found from:
$z=\frac{X-\mu}{\sigma}
$
$z=\frac{5-4}{0.6}=1.667$
Reference to a normal distribution table shows that the cumulative probability for a z-score of 1.667 is around 0.9522.
Therefore the probability that a conversation lasts for longer than 5 minutes is:
1 - 0.9522 = 0.048 to 3 d.p.

8 0

4 years ago

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If you flip 11 coins, the probability of not getting all 11 tails is

Marta_Voda [28]

The probability of *NOT* getting all 11 tails is 91/100

4 0

2 years ago