The probability of an event occurring is given by the ratio of the number of
possible outcome to the number of required outcome.
- First question: The probability that the first coin lands on heads and the second coin lands on tails is <u>0.25</u>.
- Second question: The probability of drawing a black card and then a 8 is
.
- Third question: The probability that the number chosen is 4 and the letter chosen is a consonant, is
.
- Fourth question: The probability that the first die lands on an even number and the second die is less than 2, is
.
Reasons:
First question:
The number of faces in a coin = 2; A head or a tail
The probability that the first coin lands on heads, P(H) = ![\dfrac{1}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7D)
The probability that the second coin lands on tails, P(T) = ![\dfrac{1}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7D)
The probability that the first coin lands on heads and the second coin lands
on tails = P(H ∩ T)
Which gives;
![P(H \cap T) = \dfrac{1}{2} \times \dfrac{1}{2} = \dfrac{1}{4}](https://tex.z-dn.net/?f=P%28H%20%5Ccap%20T%29%20%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%20%5Ctimes%20%20%5Cdfrac%7B1%7D%7B2%7D%20%3D%20%5Cdfrac%7B1%7D%7B4%7D)
The probability that the first coin lands on heads and the second coin lands on tails =
= <u>0.25</u>
Second question:
The number of black cards in a pack of 52 = 26 cards
The number of cards that are a 8 in a pack of 52 cards = 8 cards
![\mathrm{The \ probability \ of \ drawing \ a \ black \ card}, \ P(B) = \dfrac{26}{52} = \dfrac{1}{2}](https://tex.z-dn.net/?f=%5Cmathrm%7BThe%20%5C%20probability%20%5C%20of%20%5C%20drawing%20%5C%20a%20%5C%20%20black%20%5C%20card%7D%2C%20%20%5C%20P%28B%29%20%20%3D%20%5Cdfrac%7B26%7D%7B52%7D%20%3D%20%5Cdfrac%7B1%7D%7B2%7D)
![\mathrm{The \ probability \ of \ drawing \ a \ 8,} \ P(8) = \dfrac{8}{52} = \dfrac{2}{13}](https://tex.z-dn.net/?f=%5Cmathrm%7BThe%20%5C%20probability%20%5C%20of%20%5C%20drawing%20%5C%20a%20%5C%20%208%2C%7D%20%5C%20P%288%29%20%3D%20%5Cdfrac%7B8%7D%7B52%7D%20%3D%20%5Cdfrac%7B2%7D%7B13%7D)
The probability of drawing a black card and then an 8, P(B∩8), is given as follows;
![P(B \cap 8) = \dfrac{1}{2} \times \dfrac{2}{13} = \dfrac{1}{13}](https://tex.z-dn.net/?f=P%28B%20%5Ccap%208%29%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%20%5Ctimes%20%5Cdfrac%7B2%7D%7B13%7D%20%3D%20%5Cdfrac%7B1%7D%7B13%7D)
The probability of drawing a black card and then a 8 is P(B∩8) = ![\underline{\dfrac{1}{13}}](https://tex.z-dn.net/?f=%5Cunderline%7B%5Cdfrac%7B1%7D%7B13%7D%7D)
Third question:
The probability that a number chosen between 0 and 9 is 4, P(4) = ![\dfrac{1}{9}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B9%7D)
The number of consonant in the alphabet = 21
The probability that a letter chosen from A to Z is a consonant, P(C) = ![\dfrac{21}{26}](https://tex.z-dn.net/?f=%5Cdfrac%7B21%7D%7B26%7D)
The probability that the number chosen is 4 and the letter chosen is a consonant, P(4 ∩ C) = ![\dfrac{1}{9} \times \dfrac{21}{26} = \underline{ \dfrac{21}{234}}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B9%7D%20%5Ctimes%20%5Cdfrac%7B21%7D%7B26%7D%20%3D%20%5Cunderline%7B%20%5Cdfrac%7B21%7D%7B234%7D%7D)
Fourth question:
The number of even numbers on a die = 3; (2, 4, 6)
The number of numbers less than 2 on a die = 1
The probability that the first die lands on an even number, P(E) = ![\dfrac{3}{6}](https://tex.z-dn.net/?f=%5Cdfrac%7B3%7D%7B6%7D)
The probability that the second die is less than 2. P(<2) = ![\dfrac{1}{6}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B6%7D)
Therefore;
The probability that the first die lands on an even number and the second die is less than 2, P(E ∩ <2) = ![\dfrac{3}{6} \times \dfrac{1}{6} = \dfrac{3}{36} = \underline{\dfrac{1}{12}}](https://tex.z-dn.net/?f=%5Cdfrac%7B3%7D%7B6%7D%20%5Ctimes%20%5Cdfrac%7B1%7D%7B6%7D%20%3D%20%5Cdfrac%7B3%7D%7B36%7D%20%3D%20%5Cunderline%7B%5Cdfrac%7B1%7D%7B12%7D%7D)
Learn more here:
brainly.com/question/19916581