If two people pick a number from 1 to 80, then there are 79 possible adjacent pairs that these numbers could go in. For each of these pairs, there are two options (one with person a picking the lower number and one with person b picking the lower number). Thus there are 158 possible pairs. The chance that person 1 will pick any given number is 1/80. The chance that person two will pick any given number is 1/80. Thus the probability that they have picked adjacent number is (1/80)2x158 = 0.0246875
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The probability of getting two prime numbers when two numbers are selected at random and without replacement, from 1 to 10 is 2/15.
The probability is 5/6.
I'm assuming you multiply the numbers rolled. Thus the rules of even and odd numbers come into play. The only way to get an odd product is to roll two odd numbers. The probability desired is 1 minus the probability of rolling two odd numbers. The odds of rolling an odd number is 1/2. Since the rolls are independent events, the odds of rolling two odd numbers is (1/2)2 = 1/4 So the probability of getting an even product is: 1 - 1/4 = 3/4
This depends entirely on the genotype of the parents. The probability of getting a specific genotype is the probability of getting the correct allele from mother (1/2) multiplied by the probability of getting the correct allele from father (1/2) multiplied by the number of ways this can occur. The probability of getting a phenotype, if the phenotype is dominant, is the sum of the probability of getting two dominant alleles, and the probability of getting one dominant allele. If the phenotype is recessive, the probability is equal to the probability of getting two recessive alleles.
The probability of getting a 2 or 12 on two dice is 2 in 36, or 1 in 18.