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Vaselesa [24]
2 years ago
14

Determine the following probabilities. Enter your final answers as reduced fractions. Two coins are flipped. Find the probabilit

y that the first coin land on heads and the second coin lands on heads. Two cards are drawn from a deck of 52 cards. The first card is replaced before drawing the second card. Find the probability that the first card is black and the second card is a 8. A single digit between 0 and 9 is randomly chosen, and a single letter from A to Z is randomly chosen. Find the probability that the number is 4 and the letter is a consonant. Two dice are rolled. Find the probability that first die lands on an even number and the second die is less than 2.
Mathematics
1 answer:
-Dominant- [34]2 years ago
3 0

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 \underline{\dfrac{1}{13}}.

  • Third question: The probability that the number chosen is 4 and the letter chosen is a consonant, is \underline{\dfrac{21}{234}}.

  • Fourth question: The probability that the first die lands on an even number and the second die is less than 2, is \underline{\dfrac{1}{12}}.

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}

The probability that the second coin lands on tails, P(T) = \dfrac{1}{2}

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}

The probability that the first coin lands on heads and the second coin lands on tails = \dfrac{1}{4} = <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}

\mathrm{The \ probability \ of \ drawing \ a \  8,} \ P(8) = \dfrac{8}{52} = \dfrac{2}{13}

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}

The probability of drawing a black card and then a 8 is P(B∩8) = \underline{\dfrac{1}{13}}

Third question:

The probability that a number chosen between 0 and 9 is 4, P(4) = \dfrac{1}{9}

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}

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}}

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}

The probability that the second die is less than 2. P(<2) = \dfrac{1}{6}

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}}

Learn more here:

brainly.com/question/19916581

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