Question

Q: The central angle of sector E is 71 degrees and the central angle of sector F is 39 degrees. What is the probability that the spinner does not land on sector F or E?

Answer 1

Answer:

$\sf \dfrac{25}{36}$

Step-by-step explanation:

Angles around a point sum to 360°.

Find the central angle of the sectors that are not sectors E and F.

⇒ D + H + G + E + F = 360°

⇒ D + H + G = 360° - E - F

⇒ D + H + G = 360° - 71° - 39°

⇒ D + H + G = 250°

Probability formula

$\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}$

Therefore, the probability that the spinner does not land on sector F or E is:

$\implies \sf P(not\:F\:or\:E)=\dfrac{P(D+H+G)}{360^{\circ}}$

$\implies \sf P(not\:F\:or\:E)=\dfrac{250^{\circ}}{360^{\circ}}$

$\implies \sf P(not\:F\:or\:E)=\dfrac{25}{36}$

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