We read your photo as:

A bag contains 6 balls, 4 red and 2 black. What is the probability of drawing two balls of the same color without replacement?

Mathematics

ScanSolve AI Answer

Answer

715\frac{7}{15}

Step-by-step solution

4 steps

  1. Determine the number of balls of each color.

    The bag contains a total of 6 balls.
    Number of red balls = 4.
    Number of black balls = Total balls - Red balls = 6−4=26 - 4 = 2.

  2. Calculate the probability of drawing two red balls (RR) without replacement.

    The probability of drawing the first red ball is the number of red balls divided by the total number of balls.

    P(1st Red)=46P(\text{1st Red}) = \frac{4}{6}

    After drawing one red ball, there are 3 red balls left and 5 total balls left.
    The probability of drawing the second red ball is the number of remaining red balls divided by the remaining total balls.

    P(2nd Red | 1st Red)=35P(\text{2nd Red | 1st Red}) = \frac{3}{5}

    The probability of drawing two red balls is:

    P(RR)=P(1st Red)×P(2nd Red | 1st Red)=46×35=1230=25P(RR) = P(\text{1st Red}) \times P(\text{2nd Red | 1st Red}) = \frac{4}{6} \times \frac{3}{5} = \frac{12}{30} = \frac{2}{5}

  3. Calculate the probability of drawing two black balls (BB) without replacement.

    The probability of drawing the first black ball is the number of black balls divided by the total number of balls.

    P(1st Black)=26P(\text{1st Black}) = \frac{2}{6}

    After drawing one black ball, there is 1 black ball left and 5 total balls left.
    The probability of drawing the second black ball is the number of remaining black balls divided by the remaining total balls.

    P(2nd Black | 1st Black)=15P(\text{2nd Black | 1st Black}) = \frac{1}{5}

    The probability of drawing two black balls is:

    P(BB)=P(1st Black)×P(2nd Black | 1st Black)=26×15=230=115P(BB) = P(\text{1st Black}) \times P(\text{2nd Black | 1st Black}) = \frac{2}{6} \times \frac{1}{5} = \frac{2}{30} = \frac{1}{15}

  4. Calculate the total probability of drawing two balls of the same color.

    The probability of drawing two balls of the same color is the sum of the probabilities of drawing two red balls or two black balls.

    P(Same Color)=P(RR)+P(BB)P(\text{Same Color}) = P(RR) + P(BB) P(Same Color)=25+115P(\text{Same Color}) = \frac{2}{5} + \frac{1}{15}

    To add these fractions, find a common denominator, which is 15.

    P(Same Color)=2×35×3+115=615+115=715P(\text{Same Color}) = \frac{2 \times 3}{5 \times 3} + \frac{1}{15} = \frac{6}{15} + \frac{1}{15} = \frac{7}{15}

    This matches option أ/.

    The final answer is 715\frac{7}{15}.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QA bag contains 3 red balls and 4 black balls. If two balls are drawn without replacement, what is…QA bag contains two black, three green and four red balls. A ball is picked from the bag at random…QA ball selected at random from a bag containing 3 red balls and 4 black balls. The first ball is not…QA bag contains 5 red, 4 blue, and 3 green balls. Three balls are drawn at random. What is the…QA bag contains 5 red balls, 3 blue balls, and 2 green balls. What is the probability of drawing a…
Browse by topic:Statistics
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.