Probabilities are used to determine the chances of events
(a) Coins
In a coin, the probability of the likely outcomes in each flip are:
Head = 1/2
Tail = 1/2
So, the probability that the first lands on head, while the second lands on tail is:
[tex]\mathbf{Pr = \frac 12 \times \frac 12}[/tex]
[tex]\mathbf{Pr = \frac 14}[/tex]
The probability that the first lands on head, while the second lands on tail is 1/4
(b) Deck of cards
There are 52 cards in a deck, 13 of which are hearts while 4 are jack.
The probability that the first card is heart is 13/52
The probability that the second card is jack is 4/51
So, the probability that the first selected card is heart, while the second is jack is:
[tex]\mathbf{Pr = \frac{13}{52} \times \frac{4}{51}}[/tex]
[tex]\mathbf{Pr = \frac{1}{51}}[/tex]
The probability that the first selected card is heart, while the second is jack is 1/51
(c) Digits and Letters
There are 10 digits between 0 and 9, so the probability of selecting 3 is 1/10.
There are 21 consonants, so the probability of selecting a consonant is 21/26
So, the probability of selecting 3 and a consonant is:
[tex]\mathbf{Pr = \frac{1}{10} \times \frac{21}{26}}[/tex]
[tex]\mathbf{Pr = \frac{21}{260}}[/tex]
The probability of selecting 3 and a consonant is 21/260
(d) Dice
There are 3 even numbers on a die; so the probability of landing on an even number is 3/6
There are 2 numbers less than 3 on a die; so the probability of landing on a number less than 3 is 2/6
So, the probability of landing on an even number and a number less than 3 is:
[tex]\mathbf{Pr = \frac 36 \times \frac 26}[/tex]
[tex]\mathbf{Pr = \frac 16}[/tex]
The probability of landing on an even number and a number less than 3 is 1/6
Read more about probabilities at:
https://brainly.com/question/11234923
