Question

Alex and James both have a bag of marbles.
* Alex's bag has 10 red marbles and 10 blue marbles.
James's bag has 15 red marbles, 10 blue marbles and 5 green marbles.
They each take a marble out of their bag without looking.
Select the statements that are correct:
-
A - They both have the same probability of picking a blue marble.
B - The probability of Alex picking a red marble is 50%.
C - They both have the same probability of picking a red marble.
D - The probability of James picking a green marble is 5%.
E - James has a higher chance of picking a red marble than Alex.

Answer 1

Answer:

[B] The probability of Alex picking a red marble is 50%.

[C] They both have the same probability of picking a red marble.

Step-by-step explanation:

Given;

Alex and James both have a bag of marbles.

Alex's bag has 10 red marbles and 10 blue marbles.

James's bag has 15 red marbles, 10 blue marbles and 5 green marbles.

They each take a marble out of their bag without looking.

Solve;

Alex have 10 Blue marbles so 10 out of 20 are Blue.

James has 10 Blue Marbles so 10 out of 30 are Blue.

Hence, [A] They both have the same probability of picking a blue marble.

is False.

Alex have 10 red and 10 blue which 10 = 10

thus, [B] The probability of Alex picking a red marble is 50%.

Alex's have 10 red marbles and James's have 15 red marbles.

10 out of 20 of them are red. Thus, that 50%

15 out of 30 of them are red. Thus, that 50%

50%  = 50%

Hence, [C] They both have the same probability of picking a red marble.

is true.

James have 15 red, 10 Blue, 5 Green marbles.

15 + 10 + 5 =30 [ Total ]

5 out of 30 is Green

5/30 = 0.16666666666

Round = 16.67%

Hence, [D]  The probability of James picking a green marble is 5%.

is False.

15 out of 30 and 10 out of 20

15/30 = 50% and 10/20 = 50%

Thus, [E] James has a higher chance of picking a red marble than Alex.

is False.

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Answer 2

Select the statements that are correct:

A - They both have the same probability of picking a blue marble. [ x ]

B - The probability of Alex picking a red marble is 50%. [✓]

C - They both have the same probability of picking a red marble. [✓]

D - The probability of James picking a green marble is 5%. [x]

E - James has a higher chance of picking a red marble than Alex. [x]

We know that ,

$probability \: \% = \frac{favourable \: outcomes}{total \: outcomes} \times 100$

Alex has↷

• 10 red marbles

$\frac{10}{20} \times 100 = 50\%$

• 10 blue marbles

$\frac{10}{20} \times 100 = 50\%$

James has ↷

• 15 red marbles

$\frac{15}{30} \times 100 = 50\%$

• 10 blue marbles

$\frac{10}{30} \times 100 = 33.33\%$

• 5 green marbles

$\frac{5}{30} \times 100 = 16.66\%$