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slava [35]
3 years ago
5

Five balls are numbered 1 through 5 and placed in a bowl. josh will randomly choose a ball from the bowl, look at its number and

then put it back into the bowl. then josh will again randomly choose a ball from the bowl and look at its number. what is the probability that the product of the two numbers will be even and greater than 10? express your answer as a common fractio
Mathematics
1 answer:
svetlana [45]3 years ago
3 0
1/5

Each of the 5 balls has 5 possible combinations, as each one (1 - 5) can be paired with any of the 5. Therefore, the total number of combinations is 25.
For the product to be even, one of the balls has to be a 2 or 4. However, 2 multiplied by any number 1 - 5 is not greater than 10, so 2 is not an option. This means one of the balls has to be a 4.
There are only 3 numbers of 1 - 5 that, when multiplied by 4, are greater than 10. These are 3, 4, and 5.
This means that there are 5 combinations that work:
3 × 4 = 12
4 × 3 = 12
4 × 4 = 16
4 × 5 = 20
5 × 4 = 20

This means that 5 out of 25 combinations produce a result that is both even and greater than 10.
5/25 is then simplified to 1/5
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4 0
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If a cat with short brown hair (llBb) is crossed with a cat with long black hair (Llbb), what is the likelihood that there will
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Bb = brown hair phenotype

bb = black hair phenotype

we see that B = brown hair is the dominant gene while b = black hair is the recessive gene

----------------------------------

ll = short hair, this is a lowercase L

Ll = long hair

In this case, l = short hair is the recessive gene while L = long hair is the dominant gene.

----------------------------------

Check out the diagram below to see the dihybrid crosses for each of the hair color and hair length genotypes. From there, I show all of the genotypes possible for any offspring. Those genotypes are

  • LlBb  = long brown hair (comes up 4 times)
  • Llbb  = long black hair (comes up 4 times)
  • llBb  = short brown hair (comes up 4 times)
  • llbb  = short black hair (comes up 4 times)

-----------------------------------

If we are talking about 1 offspring, then it is not possible for him/her to have both "long black hair AND short brown hair" as the instructions state. So let's consider two offspring instead.

The probability of having long black hair is 4/16 = 1/4 as there are 4 cases of Llbb out of 16 cases total. Similarly, the probability of getting llBb is 4/16 = 1/4 as well, for pretty much the same reasons.

The probability of having both events occur is (1/4)*(1/4) = 1/16

The multiplication of probabilities is valid because the two events are independent.

==============================================

<h3>Final Answer: A) 1/16</h3>

5 0
3 years ago
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